Go into your Shogo: MAD directory and open the "autoexec.cfg" file with the notepad and copy and paste this to the bottom of it:

rangebind "##mouse" "Wheel" 0.100000 10000.000000 "NextWeapon" -10000.000000 -0.100000 "PrevWeapon"

Confirmed, works fine.
Of course, my advice whenever applying anything like this is to back up the original copy of the file, just in case something goes awry. Still, I doubt anybody will have problems with this.
It's decent, but I still found the weapon cycling a bit slow this way. It's fine if I'm just swapping between the two automatics, though, which one does a lot of in this game.

Edit: Er, that said, go ahead and put it in the file, folks. It's not like the mouse wheel's doing much else anyway.

I tried this twice and it didn't work either time. Anyone else have this problem?

I'm guessing that your file is always missing the entry you made, after running the game.

Try running Shogo as admin. Also, on the launch menu click "Advanced..." and check "Always specify these command-line parameters". Then put in the mouse wheel bind again.

BTW, this is how my autoexec.cfg's mouse settings look like. Go ahead and copy + paste these stuff over the mouse part of the file.

enabledevice "##mouse"
rangebind "##mouse" "Y-axis" 0.000000 0.000000 "Axis2"
scale "##mouse" "Y-axis" 0.002375
rangebind "##mouse" "X-axis" 0.000000 0.000000 "Axis1"
scale "##mouse" "X-axis" 0.002375
rangebind "##mouse" "Wheel" -10000.000000 -0.100000 "PrevWeapon" 0.100000 10000.000000 "NextWeapon"
rangebind "##mouse" "Button 0" 0.000000 0.000000 "Fire"
ModelAdd 0.000000 0.000000 0.000000
ModelDirAdd 0.000000 0.000000 0.000000

Maybe this will fix your prob.